No abstract

While the use of numerical general relativity for modeling astrophysical phenomena and compact objects is commonplace, the application to cosmological scenarios is only just beginning. Here, we examine the expansion of a spacetime using the Baumgarte-Shapiro-Shibata-Nakamura formalism of numerical relativity in synchronous gauge. This work represents the first numerical cosmological study that is fully relativistic, nonlinear, and without symmetry. The universe that emerges exhibits an average Friedmann-Lemaître-Robertson-Walker (FLRW) behavior; however, this universe also exhibits locally inhomogeneous expansion beyond that expected in linear perturbation theory around a FLRW background.

First-order phase transitions are a source of stochastic gravitational radiation. Precision calculations of the gravitational waves emitted during these processes, sourced by both the degrees of freedom undergoing the transition and anisotropic stress of the coupled, ambient constituents, have reached an age of maturity. Here we present high-resolution numerical simulations of a scalar field coupled to a fluid and parameterize the final gravitational wave spectrum as a function of the ratio of the energies of the two sectors and the coupling between the two sectors for a set of models that represent different types of first-order phase transitions. In most cases, the field sector is the dominant source of gravitational radiation, but it is possible in certain scenarios for the fluid to have the most important contribution.

We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, CosmoGRaPH, which employs the BaumgarteShapiro-Shibata-Nakamura (BSSN) formalism on a 3-dimensional grid. Using CosmoGRaPH, we calculate the effect of an inhomogeneous matter distribution on the evolution of a spacetime. We also present the results of a set of standard stability tests to demonstrate the robustness of our simulations.

How does inhomogeneity affect our interpretation of cosmological observations? It has long been wondered to what extent the observable properties of an inhomogeneous universe differ from those of a corresponding Friedman-Lemaitre-Robertson-Walker (FLRW) model, and how the inhomogeneities affect that correspondence. Here, we use numerical relativity to study the behavior of light beams traversing an inhomogeneous universe and construct the resulting Hubble diagrams. The universe that emerges exhibits an average FLRW behavior, but inhomogeneous structures contribute to deviations in observables across the observer's sky. We also investigate the relationship between angular diameter distance and the angular extent of a source, finding deviations that grow with source redshift. These departures from FLRW are important path-dependent effects with implications for using real observables in an inhomogeneous universe such as our own.